Question

Rationalize the denominator of 3√2/3√2-2√3

Answer 1

Answer :

= 3 + √6

Step-by-step explanation :

       $\underline{\underline{\bf Rationalizing \ factor:}}$

 $\bigstar$   The factor of multiplication by which rationalization is done, is called as rationalizing factor.

 $\bigstar$   If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

 $\bigstar$   For example, rationalizing factor of (3 + √2) is (3 - √2)

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$\bf =\frac{3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}}$

Rationalizing factor = 3√2 + 2√3

$\bf =\frac{3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}} \times \frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}} \\\\\\ =\frac{3\sqrt{2}(3\sqrt{2}+2\sqrt{3})}{(3\sqrt{2}-2\sqrt{3})(3\sqrt{2}+2\sqrt{3})} \\\\\\ =\frac{9(\sqrt{2})^2+6\sqrt{6}}{(3\sqrt{2})^2-(2\sqrt{3})^2} \\\\\\ =\frac{9(2)+6\sqrt{6}}{9(2)-4(3)} \\\\\\ =\frac{18+6\sqrt{6}}{18-12} \\\\\\ =\frac{6(3+\sqrt{6})}{6} \\\\\\ =3+\sqrt{6}$

Answer 2

Step-by-step explanation:

Refer the attachment......

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